Employee Churn

#loading the required libraries
library(mlr)
library(survival)
library(pec)
library(survAUC)
library(dplyr)
library(reshape2)
library(ggplot2)
library(plyr)
library(reshape2)
library(plotly)
library(corrplot)
library(ggcorrplot)
library(randomForestSRC)

step 1: Loading the data

Employees=read.csv("turnover.csv")
Employeess = Employees
Employees

step 2: Data manipulation and Exploratory Data Analysis

#removing null values
Employees=na.omit(Employees)

# Summary statistics
summary(Employees)

      stag              event           gender               age          industry          profession          traffic         
 Min.   :  0.3942   Min.   :0.0000   Length:1129        Min.   :18.00   Length:1129        Length:1129        Length:1129       
 1st Qu.: 11.7289   1st Qu.:0.0000   Class :character   1st Qu.:26.00   Class :character   Class :character   Class :character  
 Median : 24.3450   Median :1.0000   Mode  :character   Median :30.00   Mode  :character   Mode  :character   Mode  :character  
 Mean   : 36.6275   Mean   :0.5058                      Mean   :31.07                                                           
 3rd Qu.: 51.3183   3rd Qu.:1.0000                      3rd Qu.:36.00                                                           
 Max.   :179.4497   Max.   :1.0000                      Max.   :58.00                                                           
    coach           head_gender          greywage             way             extraversion       independ       selfcontrol    
 Length:1129        Length:1129        Length:1129        Length:1129        Min.   : 1.000   Min.   : 1.000   Min.   : 1.000  
 Class :character   Class :character   Class :character   Class :character   1st Qu.: 4.600   1st Qu.: 4.100   1st Qu.: 4.100  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character   Median : 5.400   Median : 5.500   Median : 5.700  
                                                                             Mean   : 5.592   Mean   : 5.478   Mean   : 5.597  
                                                                             3rd Qu.: 7.000   3rd Qu.: 6.900   3rd Qu.: 7.200  
                                                                             Max.   :10.000   Max.   :10.000   Max.   :10.000  
    anxiety          novator     
 Min.   : 1.700   Min.   : 1.00  
 1st Qu.: 4.800   1st Qu.: 4.40  
 Median : 5.600   Median : 6.00  
 Mean   : 5.666   Mean   : 5.88  
 3rd Qu.: 7.100   3rd Qu.: 7.50  
 Max.   :10.000   Max.   :10.00  

# Structure of the data
str(Employees)

'data.frame':   1129 obs. of  16 variables:
 $ stag        : num  7.03 22.97 15.93 15.93 8.41 ...
 $ event       : int  1 1 1 1 1 1 1 1 1 1 ...
 $ gender      : chr  "m" "m" "f" "f" ...
 $ age         : num  35 33 35 35 32 42 42 28 29 30 ...
 $ industry    : chr  "Banks" "Banks" "PowerGeneration" "PowerGeneration" ...
 $ profession  : chr  "HR" "HR" "HR" "HR" ...
 $ traffic     : chr  "rabrecNErab" "empjs" "rabrecNErab" "rabrecNErab" ...
 $ coach       : chr  "no" "no" "no" "no" ...
 $ head_gender : chr  "f" "m" "m" "m" ...
 $ greywage    : chr  "white" "white" "white" "white" ...
 $ way         : chr  "bus" "bus" "bus" "bus" ...
 $ extraversion: num  6.2 6.2 6.2 5.4 3 6.2 6.2 3.8 8.6 5.4 ...
 $ independ    : num  4.1 4.1 6.2 7.6 4.1 6.2 6.2 5.5 6.9 5.5 ...
 $ selfcontrol : num  5.7 5.7 2.6 4.9 8 4.1 4.1 8 2.6 3.3 ...
 $ anxiety     : num  7.1 7.1 4.8 2.5 7.1 5.6 5.6 4 4 7.9 ...
 $ novator     : num  8.3 8.3 8.3 6.7 3.7 6.7 6.7 4.4 7.5 8.3 ...

# converting the data type to int
Employees$age <- as.integer(Employees$age)
head(Employees)

attach(Employees)
table(gender)

gender
  f   m 
853 276 

table(event)

event
  0   1 
558 571 

table(industry)

industry
         HoReCa     Agriculture           Banks        Building         Consult             etc              IT     manufacture 
             11              15             114              41              74              94             122             145 
         Mining          Pharma PowerGeneration      RealEstate          Retail           State         Telecom       transport 
             24              20              38              13             289              55              36              38 

table(profession)

profession
         Accounting BusinessDevelopment          Commercial             Consult            Engineer                 etc             Finance 
                 10                  27                  23                  25                  15                  37                  17 
                 HR                  IT                 Law              manage           Marketing                  PR               Sales 
                757                  74                   7                  22                  31                   6                  66 
           Teaching 
                 12 

table(greywage)

greywage
 grey white 
  127  1002 

table(way)

way
 bus  car foot 
 681  331  117 

detach(Employees)

Label encoding to change the categorical to numerical to feed into our model.

# Gender: Male/Female
Employees$gender=revalue(Employees$gender,c('m' = 0, 'f' = 1))
Employees$gender=as.numeric((Employees$gender))

# Industry: Describes what industry they belong to
Employees$industry=revalue(Employees$industry,c('Retail'= 10, 'manufacture'= 14, 'IT'= 5, 'Banks'= 2, 'etc'= 13, 'Consult'= 4, 'State'= 11, 'Building'= 3, 'PowerGeneration'= 8, 'transport'= 15, 'Telecom'= 12, 'Mining'= 6, 'Pharma'= 7, 'Agriculture'= 1, 'RealEstate'= 9, ' HoReCa'= 0))
Employees$industry=as.numeric((Employees$industry))

# Profession: Describes their respective profession
Employees$profession=revalue(Employees$profession,c('HR'=6, 'IT'= 7, 'Sales'= 11, 'etc'= 13, 'Marketing'= 9, 'BusinessDevelopment'= 1, 'Consult'= 3, 'Commercial'= 2, 'manage'= 14, 'Finance'= 5, 'Engineer'= 4, 'Teaching'= 12, 'Accounting'= 0, 'Law'= 8, 'PR'= 10))
Employees$profession=as.numeric((Employees$profession))

# Traffic: Describes what pipeline the employee came into the company
Employees$traffic=revalue(Employees$traffic,c('youjs'= 7, 'empjs'= 2, 'rabrecNErab'= 4, 'friends'= 3, 'referal'= 6, 'KA'= 0, 'recNErab'= 5, 'advert'= 1))
Employees$traffic=as.numeric((Employees$traffic))

# Coach: Describes if they had a coach in their probation period
Employees$coach=revalue(Employees$coach,c('no'= 1, 'my head'= 0, 'yes'= 2))
Employees$coach=as.numeric((Employees$coach))

# Head Gender: Gender of their coach during probation.
Employees$head_gender=revalue(Employees$head_gender,c('m' = 0, 'f' = 1))
Employees$head_gender=as.numeric((Employees$head_gender))

# Grey wage: white - taxed, grey - not taxed 
Employees$greywage=revalue(Employees$greywage,c('white'= 1, 'grey'= 0))
Employees$greywage=as.numeric((Employees$greywage))

# Way: Describes the way employee travels to office.
Employees$way=revalue(Employees$way,c(
'bus'= 0, 'car'= 1, 'foot'= 2))
Employees$way=as.numeric((Employees$way))

# Stag: Experience in months, now converted to years
#Employees$stag = Employees$stag/12

head(Employees, 10)

Employees <- Employees %>%
    rename(
        supervisor = coach,
        supervisor_gender = head_gender,
        independence = independ,
        innovator = novator
        )

head(Employees)

EAD

# Correlation Plot
var1=Employees[, !colnames(Employees) %in% "event"]
var2=Employees$event
cor_matrix=cor(Employees)
reshaping=melt(cor_matrix)
ggplot(reshaping, aes(x=Var1, y=Var2, fill=value)) +
  geom_tile() +
  scale_fill_gradient(low="white", high="blue") +
  theme_minimal() +
  theme(axis.text.x = element_text(angle = 45, vjust = 1,
                                    size = 10, hjust = 1))

#corrplot(Employees, method = 'color')
# corr <- round(cor(Employees), 1)
# ggcorrplot(corr, method = 'square')

#distribution of employees as per their experience in months 
num_bins <- 16
hist(Employees$stag, breaks = num_bins, main = "Histogram", xlab = "Experience in months", ylab = "Frequency",col = 'blue')

We could see there are more employees with experience less than 50 months.

# Lets see the distribution of employee resigning or not

# create a frequency table of the "fruit" column
df <- table(unique(Employees$event))

# plot the frequency table as a pie chart
pie(df, labels = names(df), main = "Employee Distribution")

#we could see the distribution is almost equal

We could see the distribution is almost equal.

# Create a box plot with customization
df=data.frame(Employees$age)
boxplot(df,
  main = "Box Plot",    
  xlab = "Data",        
  ylab = "Values",      
  col = "skyblue",      
  border = "black",     
  notchwidth = 0.5,     
  horizontal = FALSE   
)

# Filter data for quitting
data_event0 <- subset(Employees, event == 0)

# Filter data for not quitting
data_event1 <- subset(Employees, event == 1)

# Create box plots for event 0 and event 1
par(mfrow = c(1, 2))  # Set up a 1x2 layout for side-by-side plots
boxplot(age ~ event, data = data_event0, col = "skyblue", main = "box plot of employees who quit with age")
boxplot(age ~ event, data = data_event1, col = "lightgreen", main = "box plot of employees who stay with age")

#seeing if age influence quitting 
event_freq <- table(Employees$event,Employees$age)
my_colors <- c("skyblue", "pink")
# Create a bar plot
barplot(event_freq, beside = TRUE, legend.text = c("Event 0", "Event 1"),
        xlab = "Age", ylab = "Frequency", main = "Frequency of Events by Age",col = my_colors)

#we can see that employees from age 27-30 years tend to quit more often

We can see that employees from age 27-30 years tend to quit more often.

# Create a scatter plot with colors based on gender
p5 <-plot_ly(data = Employees, x = ~Employees$age, y = ~Employees$stag, color = ~Employees$gender)
p5

No trace type specified:
  Based on info supplied, a 'scatter' trace seems appropriate.
  Read more about this trace type -> https://plotly.com/r/reference/#scatter
No scatter mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode
No trace type specified:
  Based on info supplied, a 'scatter' trace seems appropriate.
  Read more about this trace type -> https://plotly.com/r/reference/#scatter
No scatter mode specifed:
  Setting the mode to markers
  Read more about this attribute -> https://plotly.com/r/reference/#scatter-mode

pca_fit <- prcomp(select(Employees, -c("event")), scale. = TRUE)
pca_fit

Standard deviations (1, .., p=15):
 [1] 1.4293570 1.3118447 1.1627485 1.1140314 1.0583506 1.0305625 0.9980794 0.9906903 0.9551433 0.9419927 0.9210075 0.8155224 0.7450777
[14] 0.6458678 0.4448485

Rotation (n x k) = (15 x 15):
                          PC1          PC2         PC3         PC4         PC5          PC6          PC7         PC8         PC9
stag               0.11107144  0.012015423 -0.34877227  0.49577623 -0.04395068  0.236629384  0.154203593  0.18951708 -0.49025763
gender            -0.04578407 -0.489180206 -0.04117965 -0.23820358  0.11935219  0.346059424 -0.077581624 -0.09019062  0.02631502
age                0.03561515  0.209491108  0.63900952 -0.09879427  0.06576115  0.294390654 -0.008070935 -0.04444247  0.13392075
industry           0.09494245  0.121340334 -0.05765063 -0.07964117  0.52645897  0.451471593  0.368995002 -0.10637865 -0.20687495
profession        -0.09333242  0.001971635 -0.09308453  0.14375383  0.47386001 -0.636666886  0.138319419 -0.31178586  0.01051548
traffic            0.15418091 -0.066627864 -0.24040686 -0.15414259 -0.38454895 -0.002143075  0.451827683 -0.07567782  0.39989661
supervisor        -0.07235582  0.016981392  0.12170878  0.04335960 -0.40865417  0.049183426 -0.068897796 -0.78172567 -0.41803122
supervisor_gender  0.03799404 -0.271786807 -0.34221184 -0.03803960  0.13990470  0.141699457 -0.659770926 -0.11016710  0.11151052
greywage           0.03248106 -0.108419400 -0.03129770  0.54296761 -0.22631816  0.156925365  0.078311959 -0.03533436  0.37091931
way               -0.08495950  0.137906157  0.01661898  0.42829574  0.28220367  0.212216581 -0.057010472 -0.34409067  0.43472418
extraversion      -0.49540436 -0.159210431 -0.20689294 -0.18523285  0.01314493  0.109649848  0.258694889 -0.10030939  0.06919987
independence       0.02725154 -0.441405489  0.43183090  0.32032910  0.02297193 -0.125176077 -0.027353106  0.19590048 -0.12828159
selfcontrol        0.60911671  0.095720451 -0.05290176 -0.04694869  0.02653949 -0.011512663 -0.072548941 -0.14122042  0.04935976
anxiety           -0.13073054  0.594733381 -0.17237271 -0.01660031 -0.07967463  0.054908646 -0.289810476  0.11885486  0.01962038
innovator         -0.54181910  0.097564941  0.05978231  0.12632113 -0.06881386  0.073544570 -0.065932841  0.11971822 -0.01944254
                          PC10        PC11        PC12        PC13        PC14         PC15
stag              -0.075482326  0.20368618  0.23674245 -0.39446570 -0.05421891 -0.018274338
gender            -0.022192650  0.06075502  0.67602568  0.26004107 -0.13380409 -0.067843406
age                0.055141582 -0.07256200  0.20626571 -0.60597346 -0.08584823 -0.019000217
industry           0.373581605 -0.21467109 -0.26253694  0.19894857  0.02951384  0.017759126
profession         0.193071776 -0.13667826  0.33409986 -0.20212876 -0.06724184 -0.051537468
traffic            0.499941856  0.29967411  0.03086168 -0.16955670 -0.04644295 -0.030872515
supervisor         0.093580120 -0.01822360 -0.04901220  0.06818069 -0.03970323 -0.007578446
supervisor_gender  0.309891923 -0.07022223 -0.25117420 -0.37414299  0.02077301  0.046305178
greywage           0.008609911 -0.67260777  0.08103375  0.09282492 -0.04700983  0.026846684
way               -0.213839165  0.53112594 -0.09094661  0.13452818 -0.01959072  0.012922377
extraversion      -0.355705736 -0.13057396 -0.23243247 -0.26940548 -0.05604776 -0.533684834
independence       0.317384538  0.17734182 -0.22392330  0.12210868 -0.17385121 -0.464857277
selfcontrol       -0.148475666 -0.05152735  0.10005906  0.01399600  0.49635722 -0.552316523
anxiety            0.244325040 -0.03218289  0.18160720  0.19750366 -0.42314370 -0.423768012
innovator          0.323104779  0.05510539  0.18817020  0.04843840  0.70770695 -0.046300214

summary(pca_fit)

Importance of components:
                          PC1    PC2     PC3     PC4     PC5    PC6     PC7     PC8     PC9    PC10    PC11    PC12    PC13    PC14    PC15
Standard deviation     1.4294 1.3118 1.16275 1.11403 1.05835 1.0306 0.99808 0.99069 0.95514 0.94199 0.92101 0.81552 0.74508 0.64587 0.44485
Proportion of Variance 0.1362 0.1147 0.09013 0.08274 0.07467 0.0708 0.06641 0.06543 0.06082 0.05916 0.05655 0.04434 0.03701 0.02781 0.01319
Cumulative Proportion  0.1362 0.2509 0.34107 0.42380 0.49848 0.5693 0.63569 0.70112 0.76194 0.82110 0.87765 0.92199 0.95900 0.98681 1.00000

var_explained <- (pca_fit$sdev)^2 / sum(pca_fit$sdev^2)
round(var_explained,3)

 [1] 0.136 0.115 0.090 0.083 0.075 0.071 0.066 0.065 0.061 0.059 0.057 0.044 0.037 0.028 0.013

cum_var <- cumsum(var_explained)
ggplot(data = data.frame(PC = 1:15, var_explained, cum_var), aes(x = PC)) +
  geom_line(aes(y = var_explained), color = "blue") +
  geom_line(aes(y = cum_var), color = "red") +
  xlab("Principal Component") +
  ylab("Variance Explained") +
  ggtitle("Scree Plot") +
  ylim(0, 1) +
  scale_y_continuous(labels = scales::percent) +
  theme_bw()

Scale for y is already present.
Adding another scale for y, which will replace the existing scale.

PCA can be used to reduce the dimensionality of a dataset while retaining most of its original variability. By projecting the original data onto a smaller number of dimensions, PCA can help identify underlying patterns and relationships between variables that may not be apparent in the original data.

Based on the plot, we can infer that the first principal component explains the most variance (0.136), followed by the second component (0.115), the third component (0.090), and so on.

Using the elbow method we can infer that almost all the PCs would be required to capture a significant amount of variance and hence wouldn’t be of much use in this data.

library(ggbiplot)
ggbiplot(pca_fit)

set.seed(2)
cluster_max <- 10
df_scale <- scale(Employees)
wss <- sapply(1:cluster_max, function(k){kmeans(df_scale, k, nstart=10 )$tot.withinss})
ggplot(data.frame(k=1:cluster_max, WSS=wss), aes(x=k, y=WSS)) +
  geom_point(size=2) +
  geom_line() +
  labs(title="Elbow plot", x="No. of clusters", y="WSS")

library(cluster)
gap_stat <- clusGap(df_scale, FUNcluster = kmeans, K.max = 10)

Clustering k = 1,2,..., K.max (= 10): .. done
Bootstrapping, b = 1,2,..., B (= 100)  [one "." per sample]:
.................................................. 50 
.................................................. 100 

plot(gap_stat)

library(factoextra)
fviz_nbclust(df_scale,kmeans,method="silhouette")

Taking K=3 as 3 clusters.

km_out <- kmeans(df_scale, 3)
km_out

K-means clustering with 3 clusters of sizes 402, 463, 264

Cluster means:
         stag       event     gender         age    industry   profession    traffic  supervisor supervisor_gender     greywage         way
1  0.08656047 -0.02145678  0.5222902 -0.04466913  0.21502058 -0.102296783  0.3125969 -0.09903216        0.22860888  0.009604948 -0.14773631
2 -0.12913758  0.07269125  0.5183415 -0.03165001 -0.15644380  0.008082362 -0.2203708  0.09821655        0.01078741 -0.026767500  0.06160094
3  0.09467193 -0.09481222 -1.7043666  0.12352631 -0.05304847  0.141595353 -0.0895161 -0.02145202       -0.36702780  0.032318800  0.11692713
  extraversion independence selfcontrol    anxiety   innovator
1   -0.5257387 -0.003022397   0.7639490 -0.3051783 -0.72511112
2    0.6339926  0.162648949  -0.7598591 -0.1058803  0.60702920
3   -0.3113319 -0.280649469   0.1693457  0.6503950  0.03954602

Clustering vector:
   1    2    3    4    5    6    7    8    9   10   11   12   13   14   15   16   17   18   19   20   21   22   23   24   25   26   27   28 
   3    3    2    2    3    2    2    1    2    2    2    3    2    2    2    2    2    2    2    2    1    2    2    1    1    2    2    3 
  29   30   31   32   33   34   35   36   37   38   39   40   41   42   43   44   45   46   47   48   49   50   51   52   53   54   55   56 
   1    1    2    3    1    2    2    1    2    2    2    2    1    1    1    2    1    1    2    2    2    1    2    3    2    2    2    3 
  57   58   59   60   61   62   63   64   65   66   67   68   69   70   71   72   73   74   75   76   77   78   79   80   81   82   83   84 
   3    2    2    3    2    2    1    1    1    2    1    3    3    2    2    3    2    2    2    3    2    2    2    1    1    2    2    2 
  85   86   87   88   89   90   91   92   93   94   95   96   97   98   99  100  101  102  103  104  105  106  107  108  109  110  111  112 
   2    2    1    1    2    2    2    2    3    3    1    1    1    1    1    1    2    2    2    2    2    2    1    1    1    1    2    2 
 113  114  115  116  117  118  119  120  121  122  123  124  125  126  127  128  129  130  131  132  133  134  135  136  137  138  139  140 
   3    1    3    1    1    3    3    2    1    1    2    1    2    1    1    2    2    3    3    1    3    1    3    2    2    1    2    2 
 141  142  143  144  145  146  147  148  149  150  151  152  153  154  155  156  157  158  159  160  161  162  163  164  165  166  167  168 
   2    2    2    1    1    1    1    1    1    3    2    1    2    2    3    1    2    3    3    3    2    1    1    3    1    3    2    3 
 169  170  171  172  173  174  175  176  177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192  193  194  195  196 
   3    1    3    2    2    1    2    2    2    1    1    2    3    1    3    3    3    2    2    3    1    1    1    1    2    2    1    2 
 197  198  199  200  201  202  203  204  205  206  207  208  209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 
   1    3    3    1    1    1    2    2    2    1    2    1    2    2    2    1    1    2    3    2    1    1    3    3    3    3    1    2 
 225  226  227  228  229  230  231  232  233  234  235  236  237  238  239  240  241  242  243  244  245  246  247  248  249  250  251  252 
   1    3    2    2    2    1    1    1    2    2    1    1    1    1    1    1    2    3    2    1    1    1    2    1    1    2    2    2 
 253  254  255  256  257  258  259  260  261  262  263  264  265  266  267  268  269  270  271  272  273  274  275  276  277  278  279  280 
   1    3    1    2    1    3    3    2    3    1    2    1    1    1    1    2    2    1    1    2    1    3    1    1    2    2    2    2 
 281  282  283  284  285  286  287  288  289  290  291  292  293  294  295  296  297  298  299  300  301  302  303  304  305  306  307  308 
   1    2    3    2    2    2    1    1    2    2    2    1    2    1    3    2    1    3    2    3    3    2    1    1    1    1    1    3 
 309  310  311  312  313  314  315  316  317  318  319  320  321  322  323  324  325  326  327  328  329  330  331  332  333  334  335  336 
   1    1    1    1    3    1    1    1    1    2    2    1    1    2    3    1    3    1    1    1    1    1    1    3    1    1    1    2 
 337  338  339  340  341  342  343  344  345  346  347  348  349  350  351  352  353  354  355  356  357  358  359  360  361  362  363  364 
   3    2    2    2    1    2    3    2    2    2    3    2    2    3    1    3    3    1    1    1    1    2    2    2    2    1    2    2 
 365  366  367  368  369  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384  385  386  387  388  389  390  391  392 
   2    2    1    3    1    2    2    3    3    1    1    2    2    1    3    3    3    2    2    1    2    2    2    2    2    3    1    2 
 393  394  395  396  397  398  399  400  401  402  403  404  405  406  407  408  409  410  411  412  413  414  415  416  417  418  419  420 
   1    2    1    3    1    3    2    3    2    2    1    1    2    2    3    2    3    3    2    2    3    2    3    3    1    1    1    1 
 421  422  423  424  425  426  427  428  429  430  431  432  433  434  435  436  437  438  439  440  441  442  443  444  445  446  447  448 
   2    2    1    2    2    3    1    1    1    2    2    2    2    3    2    3    3    1    2    3    2    2    1    1    1    2    2    1 
 449  450  451  452  453  454  455  456  457  458  459  460  461  462  463  464  465  466  467  468  469  470  471  472  473  474  475  476 
   3    1    1    3    2    2    2    3    3    2    2    1    2    1    1    2    2    2    1    2    2    2    2    2    2    2    1    1 
 477  478  479  480  481  482  483  484  485  486  487  488  489  490  491  492  493  494  495  496  497  498  499  500  501  502  503  504 
   1    1    1    1    3    1    1    2    2    1    1    2    3    2    2    2    1    2    1    3    2    1    3    1    1    3    2    2 
 505  506  507  508  509  510  511  512  513  514  515  516  517  518  519  520  521  522  523  524  525  526  527  528  529  530  531  532 
   1    2    2    3    2    2    1    2    2    1    3    3    2    2    2    1    2    2    1    1    1    1    1    3    2    2    1    1 
 533  534  535  536  537  538  539  540  541  542  543  544  545  546  547  548  549  550  551  552  553  554  555  556  557  558  559  560 
   2    3    3    2    2    1    2    2    2    1    1    1    3    1    1    1    1    1    1    1    3    3    1    3    1    3    1    1 
 561  562  563  564  565  566  567  568  569  570  571  572  573  574  575  576  577  578  579  580  581  582  583  584  585  586  587  588 
   3    2    1    1    2    1    2    1    3    3    1    2    3    2    2    3    2    2    3    2    3    2    2    1    2    2    2    3 
 589  590  591  592  593  594  595  596  597  598  599  600  601  602  603  604  605  606  607  608  609  610  611  612  613  614  615  616 
   2    2    2    3    3    1    2    3    2    1    1    2    1    1    1    3    1    2    2    1    2    1    2    2    2    3    2    2 
 617  618  619  620  621  622  623  624  625  626  627  628  629  630  631  632  633  634  635  636  637  638  639  640  641  642  643  644 
   1    2    1    2    2    2    2    2    2    2    3    2    2    1    1    3    2    3    1    2    1    2    2    3    2    2    1    1 
 645  646  647  648  649  650  651  652  653  654  655  656  657  658  659  660  661  662  663  664  665  666  667  668  669  670  671  672 
   3    2    2    1    1    2    3    3    2    2    1    1    1    1    1    2    2    2    1    1    1    1    2    2    1    1    1    1 
 673  674  675  676  677  678  679  680  681  682  683  684  685  686  687  688  689  690  691  692  693  694  695  696  697  698  699  700 
   3    3    3    3    2    1    1    2    2    3    2    1    1    1    1    1    2    2    2    2    2    1    2    1    1    3    3    1 
 701  702  703  704  705  706  707  708  709  710  711  712  713  714  715  716  717  718  719  720  721  722  723  724  725  726  727  728 
   2    3    2    2    2    2    2    1    1    2    2    2    3    2    2    1    1    3    3    2    2    1    2    2    2    1    2    1 
 729  730  731  732  733  734  735  736  737  738  739  740  741  742  743  744  745  746  747  748  749  750  751  752  753  754  755  756 
   2    3    1    2    3    3    3    3    1    1    1    3    2    1    3    3    2    2    2    2    1    2    3    3    1    3    1    3 
 757  758  759  760  761  762  763  764  765  766  767  768  769  770  771  772  773  774  775  776  777  778  779  780  781  782  783  784 
   3    3    3    3    3    3    3    3    3    2    2    3    3    1    3    1    3    3    1    1    3    3    3    1    1    3    1    2 
 785  786  787  788  789  790  791  792  793  794  795  796  797  798  799  800  801  802  803  804  805  806  807  808  809  810  811  812 
   2    1    2    1    3    2    2    1    1    2    2    2    1    2    2    2    1    2    2    2    1    1    2    2    2    2    2    2 
 813  814  815  816  817  818  819  820  821  822  823  824  825  826  827  828  829  830  831  832  833  834  835  836  837  838  839  840 
   1    2    1    2    1    3    2    1    1    1    1    1    1    2    3    1    3    3    1    1    2    2    2    1    3    2    2    2 
 841  842  843  844  845  846  847  848  849  850  851  852  853  854  855  856  857  858  859  860  861  862  863  864  865  866  867  868 
   3    3    3    1    2    1    3    2    3    2    1    1    1    2    1    3    3    2    2    2    2    1    1    3    3    1    1    2 
 869  870  871  872  873  874  875  876  877  878  879  880  881  882  883  884  885  886  887  888  889  890  891  892  893  894  895  896 
   1    2    3    2    1    1    2    3    1    1    1    3    2    2    2    3    3    2    3    2    1    1    2    2    2    2    1    3 
 897  898  899  900  901  902  903  904  905  906  907  908  909  910  911  912  913  914  915  916  917  918  919  920  921  922  923  924 
   2    2    1    1    1    2    2    1    1    1    1    2    1    1    2    1    2    1    1    2    2    1    1    3    1    2    1    1 
 925  926  927  928  929  930  931  932  933  934  935  936  937  938  939  940  941  942  943  944  945  946  947  948  949  950  951  952 
   2    1    1    3    1    1    1    1    2    2    2    2    2    3    1    1    3    2    2    1    1    1    1    1    3    2    1    2 
 953  954  955  956  957  958  959  960  961  962  963  964  965  966  967  968  969  970  971  972  973  974  975  976  977  978  979  980 
   3    1    3    1    2    1    2    2    3    3    1    1    2    2    1    2    3    1    3    1    1    1    3    1    2    1    3    3 
 981  982  983  984  985  986  987  988  989  990  991  992  993  994  995  996  997  998  999 1000 
   2    1    1    3    1    3    3    3    1    2    2    2    1    2    3    2    3    3    2    2 
 [ reached getOption("max.print") -- omitted 129 entries ]

Within cluster sum of squares by cluster:
[1] 5448.113 6100.411 3889.063
 (between_SS / total_SS =  14.5 %)

Available components:

[1] "cluster"      "centers"      "totss"        "withinss"     "tot.withinss" "betweenss"    "size"         "iter"         "ifault"      

ggbiplot(pca_fit,groups=km_out$cluster,scale=0)

fviz_cluster(km_out, data=df_scale)

Clustering is used to group similar observations together based on their similarity.The clusters shows us different sub-groups in our data.

Based on the clusters, we can see this trend in our data:

-Cluster 1 has a relatively higher proportion of female employees, and they are relatively younger and have a lower wage. They also tend to have higher extraversion and innovation scores, but lower self-control and anxiety scores. Additionally, they are less likely to have a supervisor, and if they do, their supervisor is more likely to be male. Employees in this cluster are more likely to quit compared to those in the other clusters.

-Cluster 2 has a higher proportion of male employees and they are relatively older with a higher wage. They tend to have higher self-control and anxiety scores but lower extraversion and innovation scores. They are less likely to have a female supervisor. Employees in this cluster are less likely to quit compared to those in Cluster 1 but more likely to quit compared to those in Cluster 3.

-Cluster 3 has a relatively higher proportion of female employees, and they are relatively older with a higher wage. They tend to have lower extraversion and innovation scores but higher self-control and anxiety scores. They are more likely to have a female supervisor. Employees in this cluster are less likely to quit compared to those in the other clusters.

X <- subset(Employeess, select = -event)
y <- Employeess$event
head(X)

#Kaplan-Meier survival curve

library(survival)
fit.surv <- survfit(Surv(stag, event) ~ 1, data=Employeess)
summary(fit.surv)

Call: survfit(formula = Surv(stag, event) ~ 1, data = Employeess)

    time n.risk n.event survival  std.err lower 95% CI upper 95% CI
   0.394   1129       1   0.9991 0.000885      0.99738        1.000
   0.427   1128       1   0.9982 0.001252      0.99578        1.000
   0.756   1122       1   0.9973 0.001534      0.99434        1.000
   0.920   1119       1   0.9964 0.001773      0.99298        1.000
   1.117   1118       2   0.9947 0.002172      0.99042        0.999
   1.413   1112       1   0.9938 0.002347      0.98918        0.998
   1.478   1110       1   0.9929 0.002510      0.98797        0.998
   1.643   1109       1   0.9920 0.002663      0.98677        0.997
   1.708   1107       1   0.9911 0.002807      0.98560        0.997
   1.741   1105       1   0.9902 0.002944      0.98443        0.996
   1.807   1104       1   0.9893 0.003075      0.98328        0.995
   2.037   1097       1   0.9884 0.003202      0.98213        0.995
   2.201   1086       2   0.9866 0.003445      0.97984        0.993
   2.267   1082       1   0.9857 0.003560      0.97870        0.993
   2.431   1079       1   0.9847 0.003672      0.97757        0.992
   2.760   1076       1   0.9838 0.003781      0.97644        0.991
   2.793   1073       2   0.9820 0.003990      0.97420        0.990
   2.858   1069       2   0.9802 0.004189      0.97198        0.988
   2.990   1067       1   0.9792 0.004285      0.97088        0.988
   3.121   1066       2   0.9774 0.004469      0.96868        0.986
   3.253   1062       3   0.9746 0.004732      0.96541        0.984
   3.351   1058       1   0.9737 0.004817      0.96432        0.983
   3.417   1057       1   0.9728 0.004899      0.96324        0.982
   3.450   1056       1   0.9719 0.004981      0.96216        0.982
   3.483   1054       1   0.9710 0.005061      0.96109        0.981
   3.581   1051       4   0.9673 0.005368      0.95679        0.978
   3.811   1045       2   0.9654 0.005515      0.95466        0.976
   3.975   1041       6   0.9598 0.005933      0.94829        0.972
   4.008   1035       1   0.9589 0.005999      0.94723        0.971
   4.074   1033       1   0.9580 0.006065      0.94617        0.970
   4.337   1031       1   0.9571 0.006129      0.94512        0.969
   4.370   1030       1   0.9561 0.006194      0.94407        0.968
   4.435   1028       2   0.9543 0.006320      0.94196        0.967
   4.534   1024       2   0.9524 0.006443      0.93986        0.965
   4.961   1019       1   0.9515 0.006504      0.93881        0.964
   5.027   1014       2   0.9496 0.006626      0.93670        0.963
   5.257   1006       1   0.9486 0.006686      0.93564        0.962
   5.322   1004       1   0.9477 0.006746      0.93458        0.961
   5.388   1002       1   0.9468 0.006805      0.93352        0.960
   5.421   1001       1   0.9458 0.006863      0.93246        0.959
   5.651    996       1   0.9449 0.006922      0.93139        0.959
   5.749    994       1   0.9439 0.006980      0.93033        0.958
   5.782    991       1   0.9430 0.007038      0.92927        0.957
   5.815    990       1   0.9420 0.007095      0.92820        0.956
   5.848    989       2   0.9401 0.007207      0.92608        0.954
   6.144    982       1   0.9391 0.007263      0.92502        0.953
   6.177    981       3   0.9363 0.007428      0.92183        0.951
   6.275    977       2   0.9344 0.007535      0.91970        0.949
   6.439    974       1   0.9334 0.007588      0.91864        0.948
   6.538    973       1   0.9324 0.007641      0.91758        0.948
   6.604    972       1   0.9315 0.007693      0.91652        0.947
   6.669    971       1   0.9305 0.007745      0.91546        0.946
   7.031    966       4   0.9267 0.007949      0.91122        0.942
   7.129    962       1   0.9257 0.007998      0.91016        0.942
   7.326    955       1   0.9247 0.008049      0.90909        0.941
   7.589    953       5   0.9199 0.008294      0.90377        0.936
   7.819    948       1   0.9189 0.008341      0.90271        0.935
   7.951    940       2   0.9170 0.008437      0.90057        0.934
   8.016    937       1   0.9160 0.008485      0.89950        0.933
   8.082    936       1   0.9150 0.008532      0.89843        0.932
   8.148    935       1   0.9140 0.008579      0.89736        0.931
   8.181    933       3   0.9111 0.008718      0.89416        0.928
   8.279    928       1   0.9101 0.008763      0.89309        0.927
   8.312    927       1   0.9091 0.008809      0.89202        0.927
   8.411    925       1   0.9081 0.008854      0.89095        0.926
   8.575    923       1   0.9072 0.008899      0.88988        0.925
   8.608    922       1   0.9062 0.008943      0.88881        0.924
   8.641    921       2   0.9042 0.009032      0.88667        0.922
   8.772    918       1   0.9032 0.009075      0.88560        0.921
   8.871    914       1   0.9022 0.009119      0.88453        0.920
   8.936    913       1   0.9012 0.009162      0.88346        0.919
   8.969    912       3   0.8983 0.009291      0.88025        0.917
   9.035    909       1   0.8973 0.009333      0.87918        0.916
   9.101    905       2   0.8953 0.009417      0.87704        0.914
   9.199    901       1   0.8943 0.009459      0.87596        0.913
   9.265    900       1   0.8933 0.009500      0.87489        0.912
   9.528    896       1   0.8923 0.009542      0.87381        0.911
   9.593    895       1   0.8913 0.009583      0.87274        0.910
   9.626    894       1   0.8903 0.009624      0.87166        0.909
   9.791    890       6   0.8843 0.009866      0.86519        0.904
   9.823    884       1   0.8833 0.009906      0.86412        0.903
   9.889    883       1   0.8823 0.009945      0.86304        0.902
  10.349    878       1   0.8813 0.009984      0.86196        0.901
  10.480    876       1   0.8803 0.010023      0.86088        0.900
  10.645    869       1   0.8793 0.010063      0.85979        0.899
  10.776    868       2   0.8773 0.010141      0.85762        0.897
  10.842    866       1   0.8763 0.010180      0.85653        0.896
  10.908    865       1   0.8752 0.010219      0.85545        0.896
  10.940    864       1   0.8742 0.010257      0.85436        0.895
  11.006    863       1   0.8732 0.010295      0.85327        0.894
  11.039    862       2   0.8712 0.010370      0.85110        0.892
  11.072    860       1   0.8702 0.010407      0.85002        0.891
  11.236    859       1   0.8692 0.010444      0.84894        0.890
  11.302    857       1   0.8682 0.010481      0.84785        0.889
  11.499    856       2   0.8661 0.010555      0.84568        0.887
  11.696    850       3   0.8631 0.010664      0.84242        0.884
  11.828    842       1   0.8620 0.010700      0.84132        0.883
  11.893    839       1   0.8610 0.010737      0.84023        0.882
  11.959    837       2   0.8590 0.010809      0.83803        0.880
  11.992    835       3   0.8559 0.010916      0.83474        0.878
  12.025    832       2   0.8538 0.010987      0.83255        0.876
  12.057    830       1   0.8528 0.011021      0.83146        0.875
  12.090    829       1   0.8518 0.011056      0.83036        0.874
  12.123    828       1   0.8507 0.011090      0.82927        0.873
  12.222    827       1   0.8497 0.011125      0.82817        0.872
  12.353    822       1   0.8487 0.011159      0.82707        0.871
  12.386    821       1   0.8476 0.011193      0.82598        0.870
  12.682    817       2   0.8456 0.011262      0.82377        0.868
  12.780    815       3   0.8424 0.011363      0.82047        0.865
  12.813    812       1   0.8414 0.011396      0.81937        0.864
  12.879    811       2   0.8393 0.011462      0.81717        0.862
  12.977    809       2   0.8373 0.011527      0.81497        0.860
  13.010    807       2   0.8352 0.011591      0.81277        0.858
  13.076    805       1   0.8341 0.011623      0.81167        0.857
  13.109    804       3   0.8310 0.011718      0.80838        0.854
  13.142    801       1   0.8300 0.011749      0.80728        0.853
  13.175    800       2   0.8279 0.011811      0.80509        0.851
  13.273    798       1   0.8269 0.011842      0.80400        0.850
  13.339    797       1   0.8258 0.011872      0.80290        0.849
  13.405    796       2   0.8238 0.011933      0.80071        0.847
  13.569    794       1   0.8227 0.011963      0.79962        0.847
  13.667    793       1   0.8217 0.011993      0.79852        0.846
  13.864    791       1   0.8207 0.012022      0.79743        0.845
  13.897    790       3   0.8175 0.012111      0.79415        0.842
  14.226    785       1   0.8165 0.012140      0.79305        0.841
  14.587    777       2   0.8144 0.012199      0.79083        0.839
  14.620    775       1   0.8133 0.012229      0.78973        0.838
  14.719    774       1   0.8123 0.012258      0.78862        0.837
  14.850    773       2   0.8102 0.012316      0.78641        0.835
  14.949    771       1   0.8091 0.012345      0.78531        0.834
  14.982    770       1   0.8081 0.012373      0.78420        0.833
  15.113    768       1   0.8070 0.012402      0.78309        0.832
  15.146    765       1   0.8060 0.012431      0.78199        0.831
  15.211    762       1   0.8049 0.012459      0.78087        0.830
  15.310    761       1   0.8039 0.012488      0.77976        0.829
  15.343    760       1   0.8028 0.012516      0.77865        0.828
  15.409    758       1   0.8018 0.012544      0.77754        0.827
  15.540    757       1   0.8007 0.012572      0.77643        0.826
  15.573    756       2   0.7986 0.012628      0.77420        0.824
  15.737    749       1   0.7975 0.012656      0.77309        0.823
  15.934    747       2   0.7954 0.012712      0.77085        0.821
  16.000    744       2   0.7932 0.012767      0.76860        0.819
 [ reached getOption("max.print") -- omitted 274 rows ]

plot(fit.surv, xlab = "Months",
    ylab = "Estimated Probability of Quitting")

library(survminer)

Loading required package: ggpubr

Attaching package: ‘ggpubr’

The following object is masked from ‘package:plyr’:

    mutate


Attaching package: ‘survminer’

The following object is masked from ‘package:survival’:

    myeloma

ggsurvplot(fit = fit.surv)

From the Kaplan-Meier curve above, we can say that with time the probability of an employee decreases. We can see that it does not decrease rapidly over time.

From the graph the median survival time of an employee seems to be around 50 months.

#K-M curve stratified by gender
fit.sex <- survfit(Surv(stag, event) ~ gender, data=Employeess)
plot(fit.sex, xlab = "Months",
    ylab = "Estimated Probability of Quitting", col = c(2,4))

ggsurvplot(fit.sex,
           conf.int =T,
           xlab = "Months",
    ylab = "Estimated Probability of Survival")

#log-rank test to compare the survival of males to females, using the 
#`survdiff()` function.
logrank.test <- survdiff(Surv(stag, event) ~ gender, data=Employeess)
logrank.test

Call:
survdiff(formula = Surv(stag, event) ~ gender, data = Employeess)

           N Observed Expected (O-E)^2/E (O-E)^2/V
gender=f 853      436      420     0.614      2.35
gender=m 276      135      151     1.706      2.35

 Chisq= 2.3  on 1 degrees of freedom, p= 0.1 

logrank.test$pvalue

[1] 0.1254498

#Next, we fit  Cox proportional hazards models using the `coxph()`  function.
fit.cox <- coxph(Surv(stag, event) ~ gender, data=Employeess)
summary(fit.cox)

Call:
coxph(formula = Surv(stag, event) ~ gender, data = Employeess)

  n= 1129, number of events= 571 

            coef exp(coef) se(coef)      z Pr(>|z|)
genderm -0.15133   0.85956  0.09898 -1.529    0.126

        exp(coef) exp(-coef) lower .95 upper .95
genderm    0.8596      1.163     0.708     1.044

Concordance= 0.516  (se = 0.01 )
Likelihood ratio test= 2.4  on 1 df,   p=0.1
Wald test            = 2.34  on 1 df,   p=0.1
Score (logrank) test = 2.34  on 1 df,   p=0.1

#Regardless of which test we use, we see that there is no clear evidence for a 
#difference in survival between males and females.

Above we plotted a K-M curve stratified by gender and we can infer from the curve that there is not much difference between the probabilty of quitting between males and females over time.

Upon further performing a logrank test to compare survival rates of both genders, we can infer from the outcome that survival analysis of employee churn is not affected by the gender of the employee.

#K-M curve stratified by profession
fit.pr <- survfit(Surv(stag, event) ~ profession, data=Employeess)
plot(fit.pr, xlab = "Months",
    ylab = "Estimated Probability of Quitting", col = c(2,4))

ggsurvplot(fit.pr,
           conf.int =T,
           xlab = "Months",
    ylab = "Estimated Probability of Survival")

#log-rank test to compare the survival of different professions , using the `survdiff()` function.
plogrank.test <- survdiff(Surv(stag, event) ~ profession, data=Employeess)
plogrank.test

Call:
survdiff(formula = Surv(stag, event) ~ profession, data = Employeess)

                                 N Observed Expected (O-E)^2/E (O-E)^2/V
profession=Accounting           10        6    12.83  3.64e+00  3.81e+00
profession=BusinessDevelopment  27       16    15.90  6.28e-04  6.51e-04
profession=Commercial           23       15     9.99  2.52e+00  2.57e+00
profession=Consult              25       16    10.32  3.13e+00  3.21e+00
profession=Engineer             15       11     6.56  3.00e+00  3.05e+00
profession=etc                  37       20    16.96  5.46e-01  5.66e-01
profession=Finance              17       12    14.51  4.34e-01  4.54e-01
profession=HR                  757      357   370.58  4.98e-01  1.43e+00
profession=IT                   74       25    39.42  5.27e+00  5.69e+00
profession=Law                   7        5     4.99  4.07e-05  4.12e-05
profession=manage               22       15     8.45  5.08e+00  5.18e+00
profession=Marketing            31       21    14.32  3.11e+00  3.21e+00
profession=PR                    6        5     3.75  4.18e-01  4.23e-01
profession=Sales                66       35    34.13  2.23e-02  2.43e-02
profession=Teaching             12       12     8.30  1.65e+00  1.69e+00

 Chisq= 29.6  on 14 degrees of freedom, p= 0.009 

plogrank.test$pvalue

[1] 0.008684665

#Next, we fit  Cox proportional hazards models using the `coxph()`  function.
pfit.cox <- coxph(Surv(stag, event) ~ profession, data=Employeess)
summary(pfit.cox)

Call:
coxph(formula = Surv(stag, event) ~ profession, data = Employeess)

  n= 1129, number of events= 571 

                                coef exp(coef) se(coef)     z Pr(>|z|)   
professionBusinessDevelopment 0.7726    2.1653   0.4797 1.611  0.10726   
professionCommercial          1.1801    3.2547   0.4851 2.433  0.01498 * 
professionConsult             1.2214    3.3918   0.4824 2.532  0.01135 * 
professionEngineer            1.2919    3.6396   0.5094 2.536  0.01121 * 
professionetc                 0.9431    2.5678   0.4686 2.012  0.04417 * 
professionFinance             0.5747    1.7767   0.5019 1.145  0.25219   
professionHR                  0.7363    2.0881   0.4140 1.779  0.07532 . 
professionIT                  0.3167    1.3727   0.4565 0.694  0.48779   
professionLaw                 0.7786    2.1784   0.6082 1.280  0.20048   
professionmanage              1.3543    3.8741   0.4864 2.784  0.00537 **
professionMarketing           1.1542    3.1714   0.4649 2.483  0.01304 * 
professionPR                  1.0649    2.9007   0.6081 1.751  0.07989 . 
professionSales               0.7921    2.2080   0.4435 1.786  0.07412 . 
professionTeaching            1.1303    3.0965   0.5005 2.258  0.02393 * 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                              exp(coef) exp(-coef) lower .95 upper .95
professionBusinessDevelopment     2.165     0.4618    0.8457     5.544
professionCommercial              3.255     0.3072    1.2578     8.422
professionConsult                 3.392     0.2948    1.3176     8.731
professionEngineer                3.640     0.2748    1.3411     9.878
professionetc                     2.568     0.3894    1.0249     6.433
professionFinance                 1.777     0.5629    0.6643     4.752
professionHR                      2.088     0.4789    0.9276     4.700
professionIT                      1.373     0.7285    0.5610     3.359
professionLaw                     2.178     0.4591    0.6614     7.175
professionmanage                  3.874     0.2581    1.4932    10.051
professionMarketing               3.171     0.3153    1.2751     7.887
professionPR                      2.901     0.3447    0.8808     9.552
professionSales                   2.208     0.4529    0.9257     5.267
professionTeaching                3.097     0.3229    1.1610     8.258

Concordance= 0.558  (se = 0.011 )
Likelihood ratio test= 28.28  on 14 df,   p=0.01
Wald test            = 28.54  on 14 df,   p=0.01
Score (logrank) test = 29.5  on 14 df,   p=0.009

Above we plotted a K-M curve stratified by profession of the employee. We can see from the curves that employees from different professions have different probability of quitting over time, where some are decreasing rapidly (like IT, Law), some are decreasing at a normal rate over time.

The p-value (0.0087) observed from the log-rank test tells us that profession does help in determining the survival rate of the employee as the p-value is way below 0.05.

On fitting the Cox-proportional hazard model, it will help identify the variables that are significantly associated with the survival outcome. From the summary of the model we can see the coefficients and the p-value of different professions and infer that (the larger the coefficient and lower the p-value, the variable has more impact on the final outcome). Hence we can say that, employees from management, marketing, consulting, engineering and teaching have a higher risk of quitting compared to others.

Here the above outcomes are not completely accurate, because above we saw the number of people for each profession are not distributed equally as employees from HR are considerably more than employees from other profession.

#K-M curve stratified by industry
fit.ind <- survfit(Surv(stag, event) ~ industry, data=Employeess)
plot(fit.ind, xlab = "Months",
    ylab = "Estimated Probability of Quitting", col = c(2,4))

ggsurvplot(fit.ind,
           conf.int =T,
           xlab = "Months",
    ylab = "Estimated Probability of Survival")

#log-rank test to compare the survival various industries, using the `survdiff()` function.
ilogrank.test <- survdiff(Surv(stag, event) ~ industry, data=Employeess)
ilogrank.test

Call:
survdiff(formula = Surv(stag, event) ~ industry, data = Employeess)

                           N Observed Expected (O-E)^2/E (O-E)^2/V
industry= HoReCa          11        6     5.79   0.00779   0.00789
industry=Agriculture      15       10     4.16   8.21470   8.32018
industry=Banks           114       75    51.11  11.17213  12.32365
industry=Building         41       31    20.59   5.26931   5.49241
industry=Consult          74       45    28.17  10.06064  10.69575
industry=etc              94       54    43.61   2.47783   2.70780
industry=IT              122       34    53.53   7.12660   7.90274
industry=manufacture     145       70    76.37   0.53160   0.61763
industry=Mining           24       14    13.60   0.01187   0.01220
industry=Pharma           20       11    11.93   0.07234   0.07466
industry=PowerGeneration  38       15    18.51   0.66687   0.69303
industry=RealEstate       13        5    10.57   2.93788   3.04576
industry=Retail          289      136   165.06   5.11503   7.30153
industry=State            55       35    27.97   1.76601   1.86333
industry=Telecom          36       14    24.50   4.50264   4.77265
industry=transport        38       16    15.54   0.01341   0.01385

 Chisq= 60.9  on 15 degrees of freedom, p= 2e-07 

ilogrank.test$pvalue

[1] 1.740932e-07

#Next, we fit  Cox proportional hazards models using the `coxph()`  function.
ifit.cox <- coxph(Surv(stag, event) ~ industry, data=Employeess)
summary(ifit.cox)

Call:
coxph(formula = Surv(stag, event) ~ industry, data = Employeess)

  n= 1129, number of events= 571 

                              coef  exp(coef)   se(coef)      z Pr(>|z|)  
industryAgriculture      0.8687904  2.3840255  0.5179957  1.677   0.0935 .
industryBanks            0.3451907  1.4122593  0.4247577  0.813   0.4164  
industryBuilding         0.3681991  1.4451297  0.4466633  0.824   0.4098  
industryConsult          0.4463360  1.5625763  0.4352886  1.025   0.3052  
industryetc              0.1862531  1.2047271  0.4307377  0.432   0.6654  
industryIT              -0.4878455  0.6139477  0.4431102 -1.101   0.2709  
industrymanufacture     -0.1262863  0.8813625  0.4259822 -0.296   0.7669  
industryMining          -0.0043689  0.9956406  0.4881063 -0.009   0.9929  
industryPharma          -0.1375448  0.8714953  0.5091819 -0.270   0.7871  
industryPowerGeneration -0.2379344  0.7882544  0.4834113 -0.492   0.6226  
industryRealEstate      -0.8176897  0.4414504  0.6076191 -1.346   0.1784  
industryRetail          -0.2386062  0.7877251  0.4176653 -0.571   0.5678  
industryState            0.1857274  1.2040939  0.4421011  0.420   0.6744  
industryTelecom         -0.6189377  0.5385162  0.4890460 -1.266   0.2057  
industrytransport        0.0003095  1.0003096  0.4791301  0.001   0.9995  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                        exp(coef) exp(-coef) lower .95 upper .95
industryAgriculture        2.3840     0.4195    0.8638     6.580
industryBanks              1.4123     0.7081    0.6143     3.247
industryBuilding           1.4451     0.6920    0.6022     3.468
industryConsult            1.5626     0.6400    0.6658     3.667
industryetc                1.2047     0.8301    0.5179     2.802
industryIT                 0.6139     1.6288    0.2576     1.463
industrymanufacture        0.8814     1.1346    0.3824     2.031
industryMining             0.9956     1.0044    0.3825     2.592
industryPharma             0.8715     1.1475    0.3213     2.364
industryPowerGeneration    0.7883     1.2686    0.3056     2.033
industryRealEstate         0.4415     2.2653    0.1342     1.452
industryRetail             0.7877     1.2695    0.3474     1.786
industryState              1.2041     0.8305    0.5062     2.864
industryTelecom            0.5385     1.8570    0.2065     1.404
industrytransport          1.0003     0.9997    0.3911     2.558

Concordance= 0.58  (se = 0.014 )
Likelihood ratio test= 57.67  on 15 df,   p=6e-07
Wald test            = 58.23  on 15 df,   p=5e-07
Score (logrank) test = 60.97  on 15 df,   p=2e-07

Above we plotted a K-M curve stratified by industry of the employee. We can see from the curves that employees from different industries have different probability of quitting over time, where some are decreasing rapidly (Agriculture), some are decreasing at a normal rate over time and some industries (Retail) remain constant after some time period.

The p-value (1.740932e-07) observed from the log-rank test tells us that industry does help in determining the survival rate of the employee as the p-value is way below 0.05.

On fitting the Cox-proportional hazard model, it will help identify the variables that are significantly associated with the survival outcome. From the summary of the model we can see the coefficients and the p-value of different industries and infer that (the larger the coefficient and lower the p-value, the variable has more impact on the final outcome). Hence we can say that, employees from Real Estate, Telecom and Retail industry do not have a higher risk of quitting compared to other industries.

#K-M curve stratified by way of transportation
fit.way <- survfit(Surv(stag, event) ~ way, data=Employeess)
plot(fit.way, xlab = "Months",
    ylab = "Estimated Probability of Quitting", col = c(2,4))

ggsurvplot(fit.way,
           conf.int =T,
           xlab = "Months",
    ylab = "Estimated Probability of Survival")

#log-rank test to compare the survival of males to females, using the `survdiff()` function.
wlogrank.test <- survdiff(Surv(stag, event) ~ way, data=Employeess)
wlogrank.test

Call:
survdiff(formula = Surv(stag, event) ~ way, data = Employeess)

           N Observed Expected (O-E)^2/E (O-E)^2/V
way=bus  681      354    316.7      4.39     10.06
way=car  331      174    194.0      2.06      3.19
way=foot 117       43     60.3      4.95      5.55

 Chisq= 11.6  on 2 degrees of freedom, p= 0.003 

wlogrank.test$pvalue

[1] 0.003061535

#Next, we fit  Cox proportional hazards models using the `coxph()`  function.
wfit.cox <- coxph(Surv(stag, event) ~ way, data=Employeess)
summary(wfit.cox)

Call:
coxph(formula = Surv(stag, event) ~ way, data = Employeess)

  n= 1129, number of events= 571 

            coef exp(coef) se(coef)      z Pr(>|z|)   
waycar  -0.22575   0.79792  0.09363 -2.411  0.01590 * 
wayfoot -0.45301   0.63571  0.16180 -2.800  0.00511 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

        exp(coef) exp(-coef) lower .95 upper .95
waycar     0.7979      1.253    0.6641    0.9586
wayfoot    0.6357      1.573    0.4629    0.8729

Concordance= 0.533  (se = 0.012 )
Likelihood ratio test= 12.06  on 2 df,   p=0.002
Wald test            = 11.47  on 2 df,   p=0.003
Score (logrank) test = 11.59  on 2 df,   p=0.003

Above we plotted a K-M curve stratified by way of transportation of the employee. We can see from the curves that employees having different ways of transportation do not have much difference in rate of survival probability reduction.

The p-value (0.003) observed from the log-rank test tells us that way of transportation does help in determining the survival rate of the employee as the p-value is below 0.05.

#K-M curve stratified by employee wages.
fit.wage <- survfit(Surv(stag, event) ~ greywage, data=Employeess)
plot(fit.wage, xlab = "Months",
    ylab = "Estimated Probability of Quitting", col = c(2,4))

ggsurvplot(fit.wage,
           conf.int =T,
           xlab = "Months",
    ylab = "Estimated Probability of Survival")

#log-rank test to compare the survival employee wage, using the `survdiff()` function.
wglogrank.test <- survdiff(Surv(stag, event) ~ greywage, data=Employeess)
wglogrank.test

Call:
survdiff(formula = Surv(stag, event) ~ greywage, data = Employeess)

                  N Observed Expected (O-E)^2/E (O-E)^2/V
greywage=grey   127       73     43.2     20.47      22.3
greywage=white 1002      498    527.8      1.68      22.3

 Chisq= 22.3  on 1 degrees of freedom, p= 2e-06 

wglogrank.test$pvalue

[1] 2.27932e-06

Above we plotted a K-M curve stratified by employee wage type. We can see from the curves that employees having grey wage and white wage have different rate of probability of survival reduction over time. We can see greywage employees quitting earlier than white wage employees.

The p-value (2.27932e-06) observed from the log-rank test tells us that employee wage does help in determining the survival rate of the employee as the p-value is below 0.05.

fit.all <- coxph(Surv(stag, event) ~ gender + profession + industry + way, data=Employeess)
summary(fit.all)

Call:
coxph(formula = Surv(stag, event) ~ gender + profession + industry + 
    way, data = Employeess)

  n= 1129, number of events= 571 

                                  coef exp(coef) se(coef)      z Pr(>|z|)    
genderm                       -0.17541   0.83912  0.11854 -1.480 0.138963    
professionBusinessDevelopment  0.85119   2.34244  0.49125  1.733 0.083150 .  
professionCommercial           1.27599   3.58223  0.49325  2.587 0.009684 ** 
professionConsult              0.67774   1.96942  0.50732  1.336 0.181578    
professionEngineer             1.07415   2.92750  0.51979  2.067 0.038781 *  
professionetc                  0.69128   1.99627  0.47975  1.441 0.149609    
professionFinance              0.30228   1.35294  0.51265  0.590 0.555430    
professionHR                   0.49326   1.63765  0.42469  1.161 0.245454    
professionIT                   0.30359   1.35471  0.47031  0.646 0.518597    
professionLaw                  0.54049   1.71684  0.63843  0.847 0.397225    
professionmanage               1.29775   3.66104  0.49796  2.606 0.009158 ** 
professionMarketing            0.92119   2.51228  0.47484  1.940 0.052377 .  
professionPR                   0.94254   2.56649  0.62793  1.501 0.133346    
professionSales                0.78789   2.19874  0.45264  1.741 0.081743 .  
professionTeaching             0.68350   1.98079  0.55739  1.226 0.220106    
industryAgriculture            0.70407   2.02196  0.53819  1.308 0.190803    
industryBanks                  0.34657   1.41421  0.42548  0.815 0.415336    
industryBuilding               0.36855   1.44564  0.44934  0.820 0.412100    
industryConsult                0.41081   1.50804  0.44026  0.933 0.350758    
industryetc                    0.07040   1.07294  0.43573  0.162 0.871638    
industryIT                    -0.46401   0.62876  0.44492 -1.043 0.296995    
industrymanufacture           -0.12459   0.88286  0.42886 -0.291 0.771424    
industryMining                -0.06952   0.93285  0.50304 -0.138 0.890090    
industryPharma                -0.20312   0.81618  0.51063 -0.398 0.690781    
industryPowerGeneration       -0.29852   0.74192  0.48512 -0.615 0.538329    
industryRealEstate            -0.93382   0.39305  0.62429 -1.496 0.134700    
industryRetail                -0.33339   0.71649  0.42035 -0.793 0.427707    
industryState                  0.03227   1.03280  0.46616  0.069 0.944802    
industryTelecom               -0.66314   0.51523  0.49254 -1.346 0.178186    
industrytransport             -0.13737   0.87165  0.48201 -0.285 0.775646    
waycar                        -0.17417   0.84015  0.10104 -1.724 0.084749 .  
wayfoot                       -0.57211   0.56433  0.16791 -3.407 0.000656 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

                              exp(coef) exp(-coef) lower .95 upper .95
genderm                          0.8391     1.1917    0.6651    1.0586
professionBusinessDevelopment    2.3424     0.4269    0.8944    6.1351
professionCommercial             3.5822     0.2792    1.3624    9.4191
professionConsult                1.9694     0.5078    0.7286    5.3232
professionEngineer               2.9275     0.3416    1.0569    8.1085
professionetc                    1.9963     0.5009    0.7796    5.1119
professionFinance                1.3529     0.7391    0.4953    3.6953
professionHR                     1.6377     0.6106    0.7124    3.7646
professionIT                     1.3547     0.7382    0.5389    3.4055
professionLaw                    1.7168     0.5825    0.4912    6.0002
professionmanage                 3.6610     0.2731    1.3795    9.7157
professionMarketing              2.5123     0.3980    0.9906    6.3716
professionPR                     2.5665     0.3896    0.7496    8.7868
professionSales                  2.1987     0.4548    0.9055    5.3390
professionTeaching               1.9808     0.5048    0.6643    5.9059
industryAgriculture              2.0220     0.4946    0.7041    5.8061
industryBanks                    1.4142     0.7071    0.6142    3.2560
industryBuilding                 1.4456     0.6917    0.5992    3.4877
industryConsult                  1.5080     0.6631    0.6363    3.5740
industryetc                      1.0729     0.9320    0.4568    2.5204
industryIT                       0.6288     1.5904    0.2629    1.5038
industrymanufacture              0.8829     1.1327    0.3809    2.0461
industryMining                   0.9328     1.0720    0.3480    2.5003
industryPharma                   0.8162     1.2252    0.3000    2.2204
industryPowerGeneration          0.7419     1.3479    0.2867    1.9200
industryRealEstate               0.3930     2.5442    0.1156    1.3361
industryRetail                   0.7165     1.3957    0.3143    1.6331
industryState                    1.0328     0.9682    0.4142    2.5752
industryTelecom                  0.5152     1.9409    0.1962    1.3529
industrytransport                0.8716     1.1473    0.3389    2.2420
waycar                           0.8402     1.1903    0.6892    1.0242
wayfoot                          0.5643     1.7720    0.4061    0.7843

Concordance= 0.612  (se = 0.013 )
Likelihood ratio test= 97.32  on 32 df,   p=2e-08
Wald test            = 96.36  on 32 df,   p=2e-08
Score (logrank) test = 100.7  on 32 df,   p=5e-09

Above code helps us in understanding and identifying the variables that are significantly associated with the survival outcome.